arXiv subjects

Shahar Hod

Publications and source records attributed to Shahar Hod.

At least 19 recordsLinked to original sources

arXiv2026

Upper bounds on the force function in spatially regular self-gravitating matter configurations

We use the non-linearly coupled Einstein-matter field equations to prove four theorems that bound from above the dimensionless force function ${\cal F}=4\pi r^2\cdot p(r)$ in spatially regular curved spacetimes of spherically symmetric self-gravitating matter configurations [here $p(r)$ is the radially-dependent pressure inside the spatially regular matter configurations]. In particular, for generic (not necessarily isotropic) matter configurations it is proved that: (i) ${\cal F}\leq 2$ for matter fields that satisfy the dominant energy condition, and (ii) ${\cal F}\leq 1$ for matter fields with a non-positive energy-momentum trace. In addition, for self-gravitating isotropic matter configurations we derive the stronger upper bounds: (iii) ${\cal F}\leq 1$ for matter fields that satisfy the dominant energy condition, and (iv) ${\cal F}\leq 1/2$ for matter fields with a non-positive energy-momentum trace. Our analytically derived results are in accord with the spirit of the maximum force conjecture in general relativity.

gr-qc↗

arXiv2026

Quantitative description of cognitive fatigue in repetitive monotonous tasks

There is strong qualitative empirical evidence in the scientific literature that, due to cognitive fatigue, workers performing repetitive and monotonous tasks are characterized by a gradual deterioration in their performance abilities as the time-on-task increases, a phenomenon known as the vigilance decrement. Using a time-dependent Sisyphus random climb model, we provide a quantitative description of this intriguing phenomenon. In particular, we use analytical techniques in order to determine the success probability function $S(t;{\cal N})$ of Sisyphus workers, the time-dependent fraction of workers who succeed, after making $t$ repetitive operations or less, to complete their task by making ${\cal N}$ successful operations in a row without a single fault in between. It is explicitly shown that the functional behavior of the increasing-in-time one-operation tumble probability $1-s(t)$ of exhausted Sisyphus workers may have a dramatic effect on the probability of the workers to achieve their ultimate goal in repetitive monotonous processes. In particular, we prove that the Sisyphus random climb model with the inverse power law functional behavior $s(t)\sim t^{-1/{\cal N}}$ of the one-operation success probability marks the boundary between Sisyphus workers whose success functions $S[t;s(t),{\cal N}]$ approach $1$ asymptotically in time (implying that all the workers eventually complete their task) and Sisyphus workers whose success functions approach an asymptotic value which is less than $1$, in which case some of the exhausted Sisyphus workers never complete their task successfully.

cond-mat.stat-mech↗

arXiv2026

Dyonic black holes supporting nearly-black self-gravitating thin shells

It has recently been revealed that dyonic black-hole spacetimes of a quasitopological non-linear electrodynamic field theory may be characterized by discrete radial regions with the property $dg_{tt}(r)/dr=0$ in which spherically symmetric massive {\it test} shells (Dyson shells with negligible self-gravity) can be supported in static equilibrium states. In the present paper we prove that the dyonic spacetimes of the non-linear electrodynamic field theory may also be characterized by the presence of radial regions with the dimensionless property $d[r\cdot g_{tt}(r)]/dr\to0^+$ in which massive {\it self-gravitating} thin shells that are on the verge of becoming black holes can be supported in static equilibrium states. Intriguingly, it is proved that the discrete radii of these self-gravitating nearly-black Dyson shells are universal in the sense that they are independent of the masses of the central supporting dyonic compact objects.

gr-qc↗

arXiv2026

Lower bound on the radii of black-hole shadows

The non-linearly coupled Einstein-matter field equations predict the existence of shadows with well-defined boundaries around black holes. We prove that, in spherically symmetric hairy black-hole spacetimes whose matter fields satisfy the weak energy condition, the radii of these shadows are bounded from below by the dimensionless relation $r_{\text{sh}}/r_{\text{H}}\geq 3\sqrt{3}/2$, where $r_{\text{H}}$ is the horizon radius of the central hairy black hole. The characteristic shadow of the (bald) Schwarzschild black-hole spacetime saturates the analytically derived lower bound.

gr-qc↗

arXiv2025

Comment on "Charged scalar field at future null infinity via nonlinear hyperboloidal evolution" [Phys. Rev. D {\bf 112}, 104053 (2025), arXiv:2506.15311]

The asymptotically decaying tails that characterize the late-time dynamics of collapsing self-gravitating charged massless scalar fields were studied three decades ago by Hod and Piran (HP). In particular, it was shown, both analytically and numerically, that the late-time behavior of these collapsing charged massless scalar fields is governed by oscillatory inverse power law tails, which decay more slowly than the familiar tails of neutral massless fields. Recently \'Alvares and Va\~no-Vi\~nuales (AVV) have investigated the same model numerically. While most of their results are in very good agreement with the earlier findings of HP, there are also some discrepancies between the original results of HP and those reported by AVV. In this compact comment, we wish to highlight a number of inaccurate claims and critical errors in the analysis and results presented by AVV.

gr-qc↗

arXiv2025

Long-lived resonances of massive scalar fields in the Reissner-Nordstr\"om black-hole spacetime: Analytic treatment in the large-mass regime

The physical and mathematical properties of the composed Reissner-Nordstr\"om-black-hole-massive-scalar-field system are studied {\it analytically} in the dimensionless large-mass $M\mu\gg1$ regime [here $\{M,\mu\}$ are respectively the mass of the central black hole and the proper mass of the scalar field]. It is proved that, for a given value ${\bar Q}\equiv Q/M$ of the dimensionless charge parameter of the central black hole, the system is characterized by the presence of quasi-resonances, linearized perturbation modes with arbitrarily long lifetimes. In particular, using analytical techniques, we determine the black-hole-field critical mass spectrum $\{M\mu_{\text{crit}}({\bar Q})\}$ which characterizes the long-lived resonances of the composed physical system.

gr-qc↗

arXiv2025

Ultra-relativistic journeys through compact astrophysical objects

It has recently been proved that, for constant density stars, there is a critical value $\Lambda^{*}=1$ for the dimensionless density parameter $\Lambda\equiv 4\pi R^2\rho_{\text{max}}$ of the star above which the asymptotically measured travel time $T_{\text{s}}$ along a semi-circular trajectory that connects two antipodal points on the surface of the star is {\it shorter} than the travel time $T_{\text{c}}$ along the (shorter) straight-line trajectory that connects the two antipodal points through the center of the compact star [here $\{R,\rho_{\text{max}}\}$ are respectively the radius and the maximum density of the compact astrophysical object]. This intriguing observation provides a nice illustration of the general relativistic time dilation (redshift) effect in highly curved spacetimes. One expects that generic compact astrophysical objects whose dimensionless density parameters are smaller than some critical value $\Lambda^*$ would be characterized by the `normal' relation $T_{\text{c}}\leq T_{\text{s}}$ for the travel times between the two antipodal points. Motivated by this expectation, in the present paper we prove, using analytical techniques, that spherically symmetric compact astrophysical objects whose dimensionless density parameters are bounded from above by the model-independent relation $\Lambda\leq\Lambda^*={3\over2}[1-({{2}\over{\pi}})^{2/5}]$ are always (regardless of their inner density profiles) characterized by the normal dimensionless ratio $T_{\text{c}}/T_{\text{s}}\leq1$.

gr-qc↗

arXiv2025

Lower bound on the proper lengths of stationary bound-state charged massive scalar clouds

It has recently been revealed that charged scalar clouds, spatially regular matter configurations which are made of linearized charged massive scalar fields, can be supported by spinning and charged Kerr-Newman black holes. Using analytical techniques, we establish a no-short hair theorem for these stationary bound-state field configurations. In particular, we prove that the effective proper lengths of the supported charged massive scalar clouds are bounded from below by the remarkably compact dimensionless relation $\ell/M>\ln(3+\sqrt{8})$, where $M$ is the mass of the central supporting black hole. Intriguingly, this lower bound is universal in the sense that it is valid for all Kerr-Newman black-hole spacetimes [that is, in the entire regime $\{a/M\in(0,1],Q/M\in[0,1)\}$ of the dimensionless spin and charge parameters that characterize the central supporting black holes] and for all values of the physical parameters (electric charge $q$, proper mass $\mu$, and angular harmonic indexes $\{l,m\}$) that characterize the supported stationary bound-state scalar fields.

gr-qc↗

arXiv2025

Marginally stable Schwarzschild-black-hole-non-minimally-coupled-Proca-field bound-state configurations

It has recently been revealed that, in curved black-hole spacetimes, non-minimally coupled massive Proca fields may be characterized by the existence of poles in their linearized perturbation equations and may therefore develop exponentially growing instabilities. Interestingly, recent numerical computations [H. W. Chiang, S. Garcia-Saenz, and A. Sang, arXiv:2504.04779] have provided compelling evidence that the onset of monopole instabilities in the composed black-hole-field system is controlled by the dimensionless physical parameter $\mu r_-$, where $\mu$ is the proper mass of the non-minimally coupled Proca field and $r_-\equiv (-2\alpha)^{1/3}r_{\text{H}}$ is the radial location of the pole [here $\alpha$ is the non-minimal coupling parameter of the Einstein-Proca theory and $r_{\text{H}}$ is the radius of the black-hole horizon]. In the present paper we use {\it analytical} techniques in order to explore the physical properties of critical (marginally-stable) composed Schwarzschild-black-hole-nonminimally-coupled-monopole-Proca-field configurations. In particular, we derive a remarkably compact analytical formula for the discrete spectrum $\{\mu(r_{\text{H}},r_-;n) \}^{n=\infty}_{n=1}$ of Proca field masses which characterize the critical black-hole-monopole-Proca-field configurations in the dimensionless regime ${{r_- -r_{\text{H}}}\over{r_{\text{H}}}}\ll1$ of near-horizon poles. The physical significance of the analytically derived resonance spectrum stems from the fact that the critical field mass $\mu_{\text{c}}\equiv\mu(r_{\text{H}},r_-;n=1)$ marks the onset of instabilities in the Schwarzschild-black-hole-nonminimally-coupled-monopole-Proca-field system. In particular, composed black-hole-linearized-Proca-field configurations in the small-mass regime $\mu\leq\mu_{\text{c}}$ of the Proca field are stable.

gr-qc↗

arXiv2025

Bound-state resonances of the Schwarzschild black hole: Analytic treatment

Inspired by an earlier idea of Mashhoon, who suggested to relate the discrete quasinormal resonant modes of a black hole to the bound-state resonances of the corresponding inverted black-hole potential, V\"olkel [Phys. Rev. Lett. {\bf 134}, 241401 (2025)] has recently computed numerically, for the first time, the bound-state energy spectrum of the inverted Schwarzschild potential. Motivated by this intriguing work, in the present work we use {\it analytical} techniques in order to explore the physical and mathematical properties of the Schwarzschild bound-state resonances. In particular, we derive closed-form compact analytical formulas for the infinite spectrum $\{E_n\}_{n=0}^{n=\infty}$ of energy eigenvalues that characterize the inverted (binding) black-hole potential. Interestingly, it is explicitly shown that our analytically derived energy spectrum of the black-hole inverted potential agrees remarkably well with the corresponding numerical data that recently appeared in the physics literature.

gr-qc↗

arXiv2025

A glimpse into the magical world of quantum gravity

In this essay it is proved that, in a self-consistent semiclassical theory of gravity, the asymptotically measured orbital periods of test particles around central compact objects are fundamentally bounded from below by the compact universal relation $T_{\infty}\geq{{2\pi e\hbar}\over{\sqrt{G}c^2 m^2_{e}}}$ [here $\{m_e,e\}$ are respectively the proper mass and the electric charge of the electron, the lightest charged particle]. The explicit dependence of the lower bound on the fundamental constants $\{G,c,\hbar\}$ of gravity, special relativity, and quantum theory suggests that it provides a rare glimpse into the yet unknown quantum theory of gravity.

gr-qc↗

arXiv2025

Curved spacetimes with continuous light disks

Highly curved spacetimes of compact astrophysical objects are known to possess light rings (null circular geodesics) with {\it discrete} radii on which massless particles can perform closed circular motions. In the present compact paper, we reveal for the first time the existence of isotropic curved spacetimes that possess light disks which are made of a {\it continuum} of closed light rings. In particular, using analytical techniques which are based on the non-linearly coupled Einstein-matter field equations, we prove that these physically intriguing spacetimes contain a central compact core of radius $r_->0$ that supports an outer spherical shell with an infinite number (a continuum) of null circular geodesic which are all characterized by the functional relations $4\pi r^2_{\gamma}p(r_{\gamma})=1-3m(r_{\gamma})/r_{\gamma}$ and $8\pi r^2_{\gamma}(\rho+p)=1$ for $r_{\gamma}\in[r_-,r_+]$ [here $\{\rho,p\}$ are respectively the energy density and the isotropic pressure of the self-gravitating matter fields and $m(r)$ is the gravitational mass contained within the sphere of radius $r$].

gr-qc↗

arXiv2025

Sisyphus random walks in the presence of moving traps

It has recently been proved that, in the presence of a static absorbing trap, Sisyphus random walkers with a restart mechanism are characterized by {\it exponentially} decreasing asymptotic survival probability functions. Interestingly, in the present compact paper we prove analytically that, in the presence of a moving trap whose velocity approaches zero asymptotically in time as $v_{\text{trap}}\sim 1/t$, the survival probabilities of the Sisyphus walkers are dramatically changed into inverse {\it power-law} decaying tails.

math.PR↗

arXiv2025

Dragging of inertial frames in the composed Kerr-Newman-orbiting-ring system

The dragging of inertial frames by an orbiting object implies that the horizon angular velocity $\Omega^{\text{BH-ring}}_{\text{H}}$ of a central black hole in a composed black-hole-orbiting-ring system is no longer related to its angular-momentum $J_{\text{H}}$ by the familiar vacuum functional relation $\Omega_{\text{H}}(J_{\text{H}})=J_{\text{H}}/M\alpha$ (here $\{M,\alpha\}$ are respectively the mass and normalized area of the central spinning black hole). Using a continuity argument, it has recently been revealed that the composed Kerr-ring system is characterized by the universal (that is, spin-{\it independent}) relation $\Delta\Omega_{\text{H}}\equiv\Omega^{\text{BH-ring}}_{\text{H}}(J_{\text{H}},J_{\text{R}},R\to R^{+}_{\text{H}})-\Omega^{\text{Kerr}}_{\text{H}}(J_{\text{H}})={{J_{\text{R}}}/{4M^3}}$, where $\{R,J_{\text{R}}\}$ are respectively the radius of the ring and its orbital angular momentum and $R_{\text{H}}$ is the horizon radius of the central Kerr black hole. This intriguing observation naturally raises the following physically interesting question: Does the physical quantity $\Delta\Omega_{\text{H}}$ in a composed black-hole-orbiting-ring system is always characterized by the near-horizon functional relation $\Delta\Omega_{\text{H}}={{J_{\text{R}}}/{4M^3}}$ which is independent of the spin (angular momentum) $J_{\text{H}}$ of the central black hole? In the present compact paper we explore the physical phenomenon of dragging of inertial frames by an orbiting ring in the composed Kerr-Newman-black-hole-orbiting-ring system. In particular, using analytical techniques, we reveal the fact that in this composed two-body (black-hole-ring) system the quantity $\Delta\Omega_{\text{H}}$ has an explicit non-trivial functional dependence on the angular momentum $J_{\text{H}}$ of the central spinning black hole.

gr-qc↗

arXiv2025

Lower bound on the radii of circular orbits in the extremal Kerr black-hole spacetime

It is often stated in the physics literature that maximally-spinning Kerr black-hole spacetimes are characterized by near-horizon co-rotating circular geodesics of radius $r_{\text{circular}}$ with the property $r_{\text{circular}}\to r^+_{\text{H}}$, where $r_{\text{H}}$ is the horizon radius of the extremal black hole. Based on the famous Thorne hoop conjecture, in the present compact paper we provide evidence for the existence of a non-trivial lower bound ${{r_{\text{circular}}-r_{\text{H}}}\over{r_{\text{H}}}}\gtrsim (\mu/M)^{1/2}$ on the radii of circular orbits in the extremal Kerr black-hole spacetime, where $\mu/M$ is the dimensionless mass ratio which characterizes the composed black-hole-orbiting-particle system.

gr-qc↗

arXiv2025

Energy spectrum of the long-range Lennard-Jones potential

The discrete energy spectra of composite inverse power-law binding potentials of the form $V(r;\alpha,\beta,n)=-\alpha/r^2+\beta/r^n$ with $n>2$ are studied {\it analytically}. In particular, using a functional matching procedure for the eigenfunctions of the radial Schr\"odinger equation, we derive a remarkably compact analytical formula for the discrete spectra of binding energies $\{E(\alpha,\beta,n;k)\}^{k=\infty}_{k=1}$ which characterize the highly-excited bound-state resonances of these long-range binding potentials. Our results are of practical importance for the physics of polarized molecules, the physics of composite polymers, and also for physical models describing the quantum interactions of bosonic particles.

quant-ph↗

arXiv2025

Survival probabilities in biased random walks: To restart or not to restart? that is the question

The time-dependent survival probability function $S(t;x_0,q)$ of biased Sisyphus random walkers, who at each time step have a finite probability $q$ to step towards an absorbing trap at the origin and a complementary probability $1-q$ to return to their initial position $x_0$, is derived {\it analytically}. In particular, we explicitly prove that the survival probability function of the walkers decays exponentially at asymptotically late times. Interestingly, our analysis reveals the fact that, for a given value $q$ of the biased jumping probability, the survival probability function $S(t;x_0,q)$ is characterized by a {\it critical} (marginal) value $x^{\text{crit}}_0(q)$ of the initial gap between the walkers and the trap, above which the late-time survival probability of the biased Sisyphus random walkers is {\it larger} than the corresponding survival probability of standard random walkers.

cond-mat.stat-mech↗

arXiv2025

A Compact theorem on the compactness of ultra-compact objects with monotonically decreasing matter fields

Self-gravitating horizonless ultra-compact objects that possess light rings have attracted the attention of physicists and mathematicians in recent years. In the present compact paper we raise the following physically interesting question: Is there a lower bound on the global compactness parameters ${\cal C}\equiv\text{max}_r\{2m(r)/r\}$ of spherically symmetric ultra-compact objects? Using the non-linearly coupled Einstein-matter field equations we explicitly prove that spatially regular ultra-compact objects with monotonically decreasing density functions (or monotonically decreasing radial pressure functions) are characterized by the lower bound ${\cal C}\geq1/3$ on their dimensionless compactness parameters.

gr-qc↗